Typically, multidimensional constellation encoding and decoding techniques involve mapping of ‘K’ bits onto ‘2K’ points in an N-dimensional Euclidean space (RN), where R denotes set of real numbers. The mapping is done in such a way that all points lie within a specified distance from a particular origin. Some of the traditional well-known constellation coding techniques utilized in the field of data transmission systems are Quadrature Phase Shift Keying (QPSK) schemes, Quadrature Amplitude Modulation (QAM) schemes, and their variants. Such schemes help to improve the reliability of the data transmission system in terms of bit error rate (BER).
Usually, the data transmission systems deploy N-dimensional Phase Shift Keying (PSK), where N is any positive integer greater than 1 or Quadrature Amplitude Modulation (QAM) constellations techniques for transmission of binary information over communication channels to combat the effects of noise over the channel. Moreover, in order to achieve better robustness against noise, the constellation symbols (also referred as points) are rearranged with ‘Gray’ coding techniques (also known as reflected binary code) to ensure that most of the adjacent symbols differ in a bit. Due to such arrangements of symbols in the constellation, the resulting coding schemes do not admit simple encoding and decoding algorithms.
Furthermore, the standard existing methods used for such coding schemes are the use of look-up tables for encoding the bits at the transmitter end and minimum distance decoding with look-up tables at the receiver end. Moreover, depending on channel conditions present in adaptive data transmission systems, the number of bits transmitted over a channel is varied. Due to variations in a number of bits, the encoding and decoding methods require too many look-up tables and take more time to encode and decode the bits.